Number of endorsements Annual salary (in millions of $) 2 3 3 12 4 3 0 10 Build a simple linear regression model to predict the annual salary of a professional athlete given their number of endorsements. Then, answer the following questions a. (4 pts.) What is the sample mean and standard deviation of the athletes' number of endorsements and annual salary? b. (2 pts.) What is the linear correlation coefficient between the athletes' number of endorsements and their annual salary? (2 pts.) What is your interpretation of the previous answer? Explain in one or two sentences (2 pts.) What are the dependent and independent variables of the model? (4 pts.) Fit the model using ordinary least squares. What are the y-intercept and the slope of the model? (4 pts.) Explain, in two or three sentences, what this y-intercept and this slope represent. (2 pts.) What is the estimated annual salary of an athlete with 3 endorsements? (4 pts.) Suppose that an athlete with 3 endorsements has an annual salary of $7.5 million What is the residual for this observation? (2 pts.) If an athlete has an annual salary of $10 million, how many endorsements do you expect this athlete to have? (6 pts.) What is the residual sum of squares, the explained sum of squares, and the total sum of squares of the model? c. d. e. f. g. h. i. j. k. (2 pts.) What is your interpretation of the previous answer? Explain in one or two sentences I. (2 pts.) What is the coefficient of determination of the model? m. (4 pts.) What is your interpretation of the previous answer? Explain in one or two sentences